Pattern formation experiments

Lead chromate is another photosensitive material which invoked many workers to carry out detailed investigation. Hatschek [68] and Das et al. [69] reported results of the light-induced periodic precipitation of lead chromate in agar-agar gel medium. In order to study the effect of light on pattern formation, experiments were done both in the presence of sunlight and in complete darkness. Homogeneous precipitation was observed when the experiment was performed in complete darkness while rhythmicity was observed in an illuminated condition. 

In order to evaluate the respective roles of gel and starch in pattern formation, experiments were performed in gel-free systems and in different types of gels [71]. In the absence of gel, the crucial problem was to avoid convection. We used a reactor made of a capillary tube closed at both ends by dialysis membranes in contact with the two chemical reservoirs. The capillary tube was filled in tiim either with polyacrylamide or agarose gel, each gel loaded with starch, or with a gel-free solution of starch. The dialysis membranes, permeable only to small molecules, maintain starch inside the capillary tube. 

Surface reconstruction of the PS-PMMA brush in selective solvents gave rise to pattern formation which was investigated by SPM, wetting experiments and XPS. The obtained morphologies depended on the thickness of the brush and its composition [283, 284] (Fig. 9.31). 

Preliminary investigations of the liquid crystal phase behavior of these gold nanoparticles initially revealed an enantiotropic nematic phase (based on polarized light optical microscopy and thermal analysis) as well as some pattern formation of the gold nanoparticles in TEM experiments [540, 541],... 

Equation (4) is thus a time-dependent boundary condition to Eqs. (6, 7), which, supplemented by the remaining boundary conditions (which also involve external constraints resulting from the operation mode of the experiment, s.b.) and possibly by the incorporation of convection, form the most basic Ansatz for modeling patterns of the reaction-transport type in electrochemical systems. However, so far, there are no studies on electrochemical pattern formation that are based on this generally applicable set of equations. Rather, one assumption was made throughout that proved to capture the essential features of pattern formation in electrochemistry and greatly simplifies the problem it is assumed that the potential distribution in the electrolyte can be calculated by Laplace s equation, i.e. Poisson s equation (6) becomes ... 

Obviously, in electrochemical experiments, the first condition is almost always fulfilled. However, the requirement of appropriate feedback mechanisms (i.e., appropriate nonlinear evolution laws) seems to constitute a severe restriction on the possible reaction mechanisms that give rise to pattern formation. From this point of view, it is astonishing that nearly all electrochemical systems exhibit dynamic instabilities. 

Section III deals with spatial phenomena. The current state of theoretical description is given in Section in.l, and experimental results are compiled in Section III.2. The organization of these two parts is analogous to Section II, that is, first waves in bistable media are discussed and then pattern formation in oscillatory media. Because the investigations of spatial self-organization are still in their infancy, not all theoretical predictions have yet been experimentally verified, and many experiments cannot yet be understood in terms of the underlying physical mechanisms. Hence this section represents a first approach toward a coherent imder-standing of spatial stractures, and a series of open questions is hsted at the end. 

An important result of the theoretical description of the electrochemical patterns discussed above was that the distance between the working electrode and the equipotential surface has an important impact on the pattern formation, or more precisely, on the range of the spatial coupling. In view of this knowledge, it is to be expected that electrode configurations different from this parallel arrangement of two equipotential surfaces affect the dynamics in a different way. An experimental setup often employed in electrochemical experiments is the use of a Haber-Luggin... 

A much-quoted experiment on pattern formation in electrochemical systems was carried out by Lev et while investigating the anodic... 

Figure 8.26. Pattern formation during the catalytic CO oxidation on the Pt(110) catalyst.(A. von Oertzen, A.S. Mikhailov, H.H. Rotermund, G. Ertl, Subsurface oxygen in the CO oxidation reaction on Pt(110) Experiments and modeling of pattern formation, Journal of Physical Chemistry B, 102 (1998) 4966).

Another set of pattern formation phenomena involve stationary, or Turing patterns (77), which arise in systems where an inhibitor species diffuses much more rapidly than an activator species. These patterns, which are often invoked as a mechanism for biological pattern formation, were first found experimentally in the chlorite-iodide-malonic acid reaction (72). Examples of typical spot and stripe patterns appear in Figure 3. Recently, experiments in reverse microemulsions have given rise not only to the waves and patterns described above, but to a variety of novel behaviors, including standing waves and inwardly moving spirals, as well (75). 

The time changes of Im(t) and qm(t) during pattern formation via SD were measured at various T by time-resolved light scattering experiments for SBR1/PB19 mixtures having near critical composition (58 wt/42 wt) (17). The results obtained were subjected to the reduced plot as shown in Fig.4 (17), in which... 

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